Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651370 | Discrete Mathematics | 2006 | 5 Pages |
Abstract
Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and term rank of G , by rk(G)rk(G) and Rk(G)Rk(G), respectively. van Nuffelen conjectured that for any graph G , χ(G)⩽rk(G)χ(G)⩽rk(G). The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G , χ(G)⩽Rk(G)χ(G)⩽Rk(G). Here we improve this upper bound and show that χl(G)⩽(rk(G)+Rk(G))/2χl(G)⩽(rk(G)+Rk(G))/2, where χl(G)χl(G) is the list chromatic number of G.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Saieed Akbari, Hamid-Reza Fanaı¨,